Advancements in Best Proximity Points: A Study in <inline-formula><math display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-Metric Spaces with Applications

Abstract

The purpose of this study is to explore the existence and uniqueness of the best proximity points for α,Θ-proximal contractions, a novel concept introduced in the context of F-metric spaces. Moreover, we provide an example to show the usability of the obtained results. To broaden the scope of this research area, we leverage our best proximity point results to demonstrate the existence and uniqueness of solutions for differential equations (equation of motion) and also for fractional differential equations.

Keywords

• best proximity point
• α,Θ-proximal contraction
• F-metric space%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="equation"><inline-formula><mml:math id="mm9842555"><mml:semantics><mml:mi mathvariant="script">F</mml:mi></mml:semantics></mml:math></inline-formula></named-content>-metric space
• nonlinear differential equation
• fractional calculus